Barack Obama has described his strategy in Afghanistan as "on track" after the US military acknowledged in a review for the president that while it may not be losing America's longest war it remains a long way from winning the conflict.

The first full-scale assessment of the president's troop surge strategy said the deadline to begin withdrawing coalition forces from Afghanistan next year will be met because of successes in reversing some of the gains made by the Taliban and against al-Qaida on the Pakistani border.

But the report acknowledged that progress is limited and fragile, and said that the challenge is to make the gains sustainable. It also recognised the role of Pakistan in sustaining the Taliban and sheltering al-Qaida but refrained from pointed accusations.

"This continues to be a very difficult endeavour but … we are on track to achieve our goals," said Obama.

The president said that the goal is to destroy al-Qaida not nation build in Afghanistan. "Today, al-Qaida's senior leadership in the border region is under more pressure than at any point since they fled Afghanistan nine years ago. Senior leaders have been killed. It's harder for them to recruit … It's harder for them to plot and launch attacks. In short, al-Qaida is hunkered down," he said.

However, the review said that in denying a safe haven to al-Qaida it was necessary "to deny the Taliban the ability to overthrow the Afghan government".

An unclassified summary of the full military review delivered to the president said that progress had been made in some areas in Afghanistan, notably with tactics such as the killing of local Taliban leaders and in weakening the insurgents' grip in the south of the country around Kandahar.

"Specific components of our strategy for Afghanistan and Pakistan are working well and there are notable operational gains. Most important, al-Qaida's senior leadership in Pakistan is weaker and under more sustained pressure than at any other point since it fled Afghanistan in 2001," the summary of the report said. "In Afghanistan, the momentum achieved by the Taliban in recent years has been arrested in much of the country and reversed in some key areas, although these gains remain fragile and reversible.

"While the strategy is showing progress across all three assessed areas of al-Qaida, Pakistan and Afghanistan, the challenge remains to make our gains durable and sustainable."

The military's assessment is more optimistic than a review of the conflict by the CIA and 15 other agencies, the US National Intelligence Estimates, which was released this week. It said the chance of success against the Taliban was limited unless Pakistan tackled the insurgents' safe havens on its territory.

Obama said that the US is pressuring the Pakistanis.

"Increasingly, the Pakistani government recognises that terrorist networks [on its borders] are a major threat to all our countries, including Pakistan," he said. "Progress has not come fast enough. We will continue to insist to Pakistani leaders that terrorist safe havens within their borders must be dealt with."

The military review acknowledged that "the denial of extremist safe havens will require greater co-operation with Pakistan along the border with Afghanistan.

"Furthermore, the denial of extremist safe havens cannot be achieved with military means alone, but must continue to be advanced by effective development strategies," it said.

The review comes amid growing scepticism among ordinary Americans over the war which has now lasted for more than nine years. Much of the popular support for the invasion has eroded as the conflict has dragged on and opinion polls now show a majority of Americans are ready to bring the troops home.

The US secretary of state, Hillary Clinton, said the administration understood public frustration but that it would be a "grave mistake" to abandon Afghanistan as the US did in the 1990s after the Soviet Union pulled out.

"I'm well aware of the popular concerns and I understand it but I don't think leaders, and certainly this president, will make decisions that are matters of life and death and the future security of our nation based on polling," she said.

Downing Street said it welcomed the US review as consistent with Britain's assessment of the conflict. "Like President Obama, we see 2011 as the year in which we have to make progress both lasting and irreversible," said the prime minister's office. "We also agree that we must use our civilian and military momentum to support a durable and favourable political resolution of the conflict."